Identifiability issues of age–period and age–period–cohort models of the Lee–Carter type
(2017) In Insurance: Mathematics and Economics 75. p.117-125- Abstract
The predominant way of modelling mortality rates is the Lee–Carter model and its many extensions. The Lee–Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in Lee–Carter models are... (More)
The predominant way of modelling mortality rates is the Lee–Carter model and its many extensions. The Lee–Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in Lee–Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.
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- author
- Beutner, Eric ; Reese, Simon LU and Urbain, Jean-Pierre
- organization
- publishing date
- 2017-07-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Age–period model, Age–period–cohort model, Identifiability, Lee–Carter model, Plug-in Lee–Carter model, Time series model
- in
- Insurance: Mathematics and Economics
- volume
- 75
- pages
- 9 pages
- publisher
- Elsevier
- external identifiers
-
- scopus:85020425752
- wos:000406983200011
- ISSN
- 0167-6687
- DOI
- 10.1016/j.insmatheco.2017.04.006
- language
- English
- LU publication?
- yes
- id
- 972206cc-0aa1-4b5c-92a0-8aaf9a647326
- date added to LUP
- 2017-06-26 14:23:14
- date last changed
- 2024-01-13 23:26:47
@article{972206cc-0aa1-4b5c-92a0-8aaf9a647326,
abstract = {{<p>The predominant way of modelling mortality rates is the Lee–Carter model and its many extensions. The Lee–Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in Lee–Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.</p>}},
author = {{Beutner, Eric and Reese, Simon and Urbain, Jean-Pierre}},
issn = {{0167-6687}},
keywords = {{Age–period model; Age–period–cohort model; Identifiability; Lee–Carter model; Plug-in Lee–Carter model; Time series model}},
language = {{eng}},
month = {{07}},
pages = {{117--125}},
publisher = {{Elsevier}},
series = {{Insurance: Mathematics and Economics}},
title = {{Identifiability issues of age–period and age–period–cohort models of the Lee–Carter type}},
url = {{http://dx.doi.org/10.1016/j.insmatheco.2017.04.006}},
doi = {{10.1016/j.insmatheco.2017.04.006}},
volume = {{75}},
year = {{2017}},
}